A general convergence result for the Ricci flow in higher dimensions

Let (M,g0) be a compact Riemannian manifold of dimension n≥4. We show that the normalized Ricci flow deforms g0 to a constant curvature metric, provided that (M,g0)×R has positive isotropic curvature. This condition is stronger than two-positive flag curvature but weaker than two-positive curvature operator